Various methods have been proposed in the prior art to electronically synthesize musical tones. One method involving frequency modulation is described in U.S. Pat. No. 4,249,447 to Tomisawa. The basic unit for accomplishing the digital frequency modulation includes an adder and a sinusoidal wave memory having values selected based on an output of the adder. In the unit, a waveform "x" represented by a sequence of digital samples is added to an output of the sinusoidal wave memory at a suitable feedback ratio. A multiplier is inserted in the feedback loop for multiplying the output of the memory, sin y, by a feedback parameter .beta.. The product of the multiplication .beta.sin y is applied to the adder which results in the expression x+.beta.sin y. The output of the adder x +.beta.sin y constitutes an input address to the sinusoidal wave memory. Partial contents of a tone wave produced by the above-described unit are controlled by changing the value of the feedback parameter .beta..
Although the device described in Tomisawa is relatively straightforward to implement, a disadvantage is that the harmonic spectrum achievable by simple multiplication is somewhat limited. In addition, for certain values of the feedback parameter, the amplitude data of both positive and negative values is alternated much too rapidly at each output sampling point of the memory causing an undesirable hunting phenomenon to occur. In order to eliminate the hunting phenomenon, an additional averaging device must be inserted in the feedback path.
Another device for generating frequency modulated music is manufactured by the AT&T Corporation under the tradename "RIO/Roadrunner". In the device, a frequency modulation algorithm is replicated utilizing floating-point DSP code. Instead of a feedback path, a large look-up table memory is used containing complex waveforms. The complex waveforms attempt to include the effect of feedback for various feedback parameters, as in Tomisawa. Due to constraints on available memory, however, limitations exist on the quality of the harmonic spectrum. Accordingly, there is a need for a device which produces a more tailored harmonic spectrum than that achievable with devices of the prior art.